Non-reflexive Relation/Examples/Arbitrary Non-reflexive Relation 1

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Example of Non-reflexive Relation

Let $V_1 = \set {y, z}$.

Let $S$ be the relation on $V_1$ defined as:

$S = \set {\tuple {y, y}, \tuple {y, z} }$

Then $S$ is neither:

a reflexive relation, as $\tuple {z, z} \notin S$


an antireflexive relation, as $\tuple {y, y} \in S$

Thus $S$ is a non-reflexive relation.